Towards practical device-independent quantum key distribution with spontaneous parametric downconversion sources, on-off photodetectors and entanglement swapping

Device-independent quantum key distribution (DIQKD) guarantees unconditional security of secret key without making assumptions about the internal workings of the devices used. It does so using the loophole-free violation of a Bell's inequality. The primary challenge in realizing DIQKD in practice is the detection loophole problem that is inherent to photonic tests of Bell's inequalities over lossy channels. We revisit the proposal of Curty and Moroder [Phys. Rev. A 84, 010304(R) (2011)] to use a linear optics-based entanglement-swapping relay (ESR) to counter this problem. We consider realistic models for the entanglement sources and photodetectors; more precisely, (a) polarization-entangled states based on pulsed spontaneous parametric downconversion (SPDC) sources with infinitely higher order multi-photon components and multimode spectral structure, and (b) on-off photodetectors with non-unit efficiencies and non-zero dark count probabilities. We show that the ESR-based scheme is robust against the above imperfections and enables positive key rates at distances much larger than what is possible otherwise.